Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability

Abstract

We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η-pairing mechanism. Our models include the SU(N) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η-pairing states in the SU(2) Hubbard model are based on the η-pairing symmetry, the exact eigenstates in the N-component system with N≥3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N-component Hubbard models for N≥3. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU(N) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators.